Yaki - a few beginner questions

For some reason I am not able to find this by searching. Anyway, I started a new game using the budget start. I selected "Terran Conflict" as one of the story states. Now I've discovered the Yaki base, have +14 relations with them, have the embassy room completed in the PHQ, but still don't see the option to invite their diplomat. Is this because I did not complete their plotline, or some other reason I am not thinking of?

Also, I want to eventually build a shipyard so the Yaki can buy ships from me. I already bought the blueprints for their faction ships. Will they order the ships then, or will this be blocked also because I did not complete their story mission?

And finally, can the Yaki ships be built using the Terran wharf/shipyard, or do they require the same components as all the other factions?

Thanks!